Answer:
[tex]a_n=3n-2[/tex]
Step-by-step explanation:
General form of an arithmetic sequence: [tex]a_n=a+(n-1)d[/tex]
where:
[tex]a_n[/tex] is the nth term[tex]a[/tex] is the first term[tex]d[/tex] is the common difference between termsCreate expressions for the 4th and 6th terms:
[tex]\implies a_4=a+(4-1)d=a+3d[/tex]
[tex]\implies a_6=a+(6-1)d=a+5d[/tex]
The ratio of the 4th term to the 6th term is 5:8, therefore:
[tex]\implies \dfrac{a_4}{a_6}=\dfrac{5}{8}[/tex]
[tex]\implies \dfrac{a+3d}{a+5d}=\dfrac{5}{8}[/tex]
[tex]\implies 8(a+3d)=5(a+5d)[/tex]
[tex]\implies 8a+24d=5a+25d[/tex]
[tex]\implies 8a-5a=25d-24d[/tex]
[tex]\implies 3a=d \quad \leftarrow \textsf{Equation 1}[/tex]
Sum of the first n terms of an arithmetic series:
[tex]S_n=\dfrac{n}{2}[2a+(n-1)d][/tex]
The sum of the first 7 terms of an arithmetic progression is 70:
[tex]\implies S_7=70[/tex]
[tex]\implies \dfrac{7}{2}[2a+(7-1)d]=70[/tex]
[tex]\implies 2a+6d=20[/tex]
[tex]\implies a+3d=10 \quad \leftarrow \textsf{Equation 2}[/tex]
Substitute Equation 1 into Equation 2 and solve for [tex]a[/tex]:
[tex]\implies a+3(3a)=10[/tex]
[tex]\implies a+9a=10[/tex]
[tex]\implies 10a=10[/tex]
[tex]\implies a=1[/tex]
Substitute found value of [tex]a[/tex] into Equation 1 and solve for [tex]d[/tex]:
[tex]\implies 3(1)=d[/tex]
[tex]\implies d=3[/tex]
Finally, substitute found values of [tex]a[/tex] and [tex]d[/tex] into the general form of the arithmetic sequence:
[tex]\implies a_n=1+(n-1)3[/tex]
[tex]\implies a_n=1+3n-3[/tex]
[tex]\implies a_n=3n-2[/tex]
Step 1: –10 + 8x < 6x – 4
Step 2: –10 < –2x – 4
Step 3: –6 < –2x
Step 4: ________
What is the final step in solving the inequality –2(5 – 4x) < 6x – 4?
x < –3
x > –3
x < 3
x > 3
x > 3
Step-by-step explanation:
The final step in solving the inequality –2(5 – 4x) < 6x – 4 is
-6/-2 < x = 3 < x
Which of the following are solutions to the inequality below? Select all that apply.
8 ≤ j j = 12 j = 5 j = 6 j =11
Answer:
j = 11
j = 12
Step-by-step explanation:
The inequality:
8 ≤ j
We will test all the options given.
-> In short, all options greater or equal to 8 will be solutions.
j = 12
8 ≤ j
8 ≤ 12 ✓
-
j = 5
8 ≤ j
8 ≤ 5 ✗
-
j = 6
8 ≤ j
8 ≤ 6 ✗
-
j =11
8 ≤ j
8 ≤ 11 ✓
Please help asap! Thanks
[tex]y=f(x)= \dfrac x 3 \\\\\text{Replace x with y and then solve for y,}\\\\~~~~x = \dfrac y 3\\\\\implies y = 3x \\\\\implies f^{-1}(x) =3x[/tex]
Points J, Q, K, and l are on the given circle. If Arc KL measures 120 degrees, and Angle KML measures 98 degrees, what is the measure of Arc JQ?
The value of the measure of Arc JQ from the given task content is; 142⁰.
What is the measure of Arc JQ?The measure of Arc JQ can be evaluated by establishing a fact that; the total angle measure in a circle by convention is; 360⁰.
On this note, it follows that the measure of Arc JQ is; 360 - 120 - 98 is; 142⁰.
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PLEASE HELP PLEASE PLEASE HELP
Answer:
2:3
Step-by-step explanation:
Simplica Los dos numeros
6 ÷ 3 = 2
9 ÷ 3 = 3
Suzy drove to a hair appointment at 50mph. Her average speed on the return home was 40mph. The return home took 1/4hr longer because of heavy traffic. How far did she travel to her hair appointment?
Since Suzy return took 1/4 hr longer, how far Suzy travelled to her appointment is 50 mi
To answer the question, we need to know what distance travelled by Suzy is
Distance between Suzy's home and hair appointmentThe distance between Suzy and her appointment is d = vt where
v = Suzy's speed = 50 mph and t = time it takes to teach her appointment.So, d = 50t (1)
Now, since Suzy returns home at a speed of v' = 40 mph and takes her 1/4 hr longer to return home,her return time is , t' = (t + 1/4) h
Since the distance she ruturns home is the same, we also have that
d = v't'
= 40(t + 1/4) (2)
Equating (1) and (2), we have
50t = 40(t + 1/4)
50t = 40t + 10
50t - 40t = 10
10t = 10
t = 10/10
t = 1 hr
How far Suzy travelled to her appointmentSubstituting t = 1 into d = 50t, we have
d = 50(1)
d = 50 m
So, how far Suzy travelled to her appointment is 50 mi
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What is the equation of the circle with a radius of 7 and center at (6, -5)?
A (x + 6)2 + (y - 5)2 = 49
B (x - 6)2 + (y + 5)2 = 7
C (x + 6)2 + (y - 5)2 = 7
D (x - 6)2 + (y + 5)2 = 49
Answer:
D is the equation of the circle
Hey everyone
This' just a random math question
[tex]x + 5 - \cfrac{1}{3} = 12[/tex]
Answer:
The value of x = 22/3
Step-by-step explanation:
x + 5 - 1/3 = 12
=> x+5 = 12 + 1/3
=> x + 5 = (36 + 1) /3
=> x + 5 = 37 /3
=> (x+5) 3 = 37
=> 3x + 15 = 37
=> 3x = 37 -15
=> 3x = 22
=> x = 22/3
Answer to your question is given in the attachment
Hope this Helps :)
Find the volume of the rectangular prism.
8 cm
10 cm
2 cm
10 cm
OA. 160.5 cm³
B. 182.4 cm³
Oc. 181.4 cm³
D. 160 cm³
2 cm
Answer:
volume= lxbxh= 10*8*2= 160 cm3
Hello all, what is 8y = 89.
Answer:
y= 11. 125
Step-by-step explanation:
8 y = 89
because you do not have another y on the other side simple divide
8 y = 89
89 / 8 = y
y= 11. 125
(Not sure what decimal place to round to so there are all 3 )
Hey there!
8y = 89
DIVIDE 8 to BOTH SIDES
8y/8 = 89/8
SIMPLIFY IT!
y = 89/8
y ≈ 11 1/8
y ≈ 11.125
Therefore, the answer is:
y = 89/8
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
I don’t understand and I need the answer
Answer:
y2 + 2y + 80
Step-by-step explanation:
Hope this helpd :) Mark brainliest?
Answer:-21
Step-by-step explanation:
-21 i think but im pretty sure
Show what you know: work out the problems below and submit a photo of your work to receive full credit.
The Florida A&M Rattlers are decorating campus for homecoming weekend. Students use 3 rolls of orange streamers for every 2 rolls of green streamers for every dorm they decorate.
Draw a model that represents the ratio of different colored streamers.
Draw a model that shows the number of orange and green streamers needed to decorate 3 dorm rooms.
The model for representing the ratio of the number of orange and green rolls are [tex]\dfrac{3}{2}[/tex].
A model that shows the number of orange and green streamers needed to decorate 3 dorm rooms will be 3O=2G
What is ratio?The ratio is defined as the representation of the one number with respect to the other number. or one number is how many times to the other number.
A model that represents the ratio of different colored streamers.
[tex]\dfrac{O}{G}=\dfrac{3}{2}[/tex]
A model that shows the number of orange and green streamers needed to decorate 3 dorm rooms.
D=3O and D=2G
3O=2G
Hence the models are [tex]\dfrac{O}{G}=\dfrac{3}{2}[/tex] and 3O=2G.
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b) In one year, Clara and Dave borrowed books from a library in the ratio 3:7. Dave borrowed 35 books. Work out the number of books borrowed by Clara.
3:7 =
3/7
3/7 = x/35
7x = 105
x = 15
answer : clara borrowed 15 books
I think it would be 15, because 3 doesn't go in evenly into 35. You might have the order of the ratio messed up.
Lorena paid $450 for a sneaker and there is a 9% advertised discount. What is the discount price?
Answer:
$40.50
Step-by-step explanation:
9% of 450 is 40.5
205000 seconds to a year
Answer:
theres 31536000 seconds in a year
Answer:
0.0065 calendar year
Step-by-step explanation:
How many seconds makes a year?
it is 31,536,000 seconds
for an approximate result, divide the time value by 3.154⁷
therefore 205000/3.154⁷
=0.00649
=0.0065
what is the measurement of angle c
Answer: 29
Step-by-step explanation:
all triangles equal to 180
180-97-54=29
How many full cases and additional items are needed to fulfill the order
There are 13 full cases and 2 additional items needed to fulfill the order
How to determine the full cases and additional items?The given parameters are:
Items ordered = 80Items per case = 6The number of cases is:
Case = 80/6
Evaluate
Case = 13 Remainder 2
This means that:
The full case is 13 and the additional item is 2
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Evaluate the difference quotient
f(x)-f(1)/X-1, where f(x)=X +5/x+1
Answer:
C) [tex]\displaystyle\frac{-2}{(x+1)}[/tex]
Step-by-step explanation:
[tex]\displaystyle \frac{f(x)-f(1)}{x-1}\\ \\\frac{\frac{x+5}{x+1}-\frac{1+5}{1+1}}{x-1}\\ \\\frac{\frac{x+5}{x+1}-\frac{6}{2}}{x-1}\\\\\frac{\frac{2(x+5)}{2(x+1)}-\frac{6(x+1)}{2(x+1)}}{x-1}\\\\\frac{\frac{2(x+5)-6(x+1)}{2(x+1)}}{x-1}\\\\\frac{\frac{2x+10-6x-6}{2(x+1)}}{x-1}\\\\\frac{\frac{-4x+4}{2(x+1)}}{x-1}\\\\\frac{\frac{-4(x-1)}{2(x+1)}}{x-1}\\\\\frac{-4}{2(x+1)}\\ \\\frac{-2}{(x+1)}[/tex]
8th grade distributive property equations and solutions
The value of x will be given as for the given expression X = -1
What is an expression?Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication and division
2x + 12 = 10
2x = 10 - 12
2x = -2
x = -1
first you distribute 2 to x and 6 which equals 2x+12=10 then you subtract 12 from 10 which equals 2x=-2 then divide -2 by 2x to see what x equals so x=-1
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The mean weight of college students is 154 lbs and the standard deviation is 3 lbs.
Assuming that the weight is normally distributed, determine the following percentages.
145 148
151
154 157 160 163
DO NOT write % in the box. It is already written outside the box for you"
The percentage of college students who weigh...
30
1)...less than 157 is
%
2) greater than 148 is
3)...between 145 and 160 is
%
%
Answer:(approx) 6.
Step-by-step explanation:Here μ=51 and σ=15
Z=
σ
X−μ
=
15
X−151
When X=120, Z=
15
120−151
=−2.067
When X=155, Z=
15
155−151
=0.2667
When X=185, Z=
15
185−151
=
15
35
=2.2667
(i) P(120<X<155)=P(−2.07<Z<0.27)
=∫
−2.067
0.2667
ϕ(z)dz=∫
0
0.2667
ϕ(z)dz+∫
0
2.0667
ϕ(z)dz
=0.4803+0.1026=0.5829.
Here N=500
∴ The number of students whose weight is between 120 and 155 pounds is
0.5872×500=291
(ii) P(X<185)=P(Z>2.27)=∫
2.2667
∞
ϕ(z)dz
=∫
0
∞
ϕ(z)dz−∫
0
2.2667
ϕ(z)dz=0.5−0.4881=0.0119
∴ the number of students with weight about 185 pounds.
=0.0119×500= (approx) 6.
The table below shows the distribution of votes for Student Government President elections.
1.What is the probability that a junior voted for Dao?
2.Voted for Wolber
3.Votes for Keegan and was from the sophomore class.
Answer:
1 out of 3 people vote for junior
Step-by-step explanation:
Simplify the equation √-42×√-30
Answer:
-6 [tex]\sqrt{35}[/tex]
Step-by-step explanation:
Answer:
[tex]6\sqrt{35}i[/tex]
Step-by-step explanation:
Find the area of the figure. Round to the nearest hundredth where necessary.
22 ft
30 ft
What is the answer?
.......................................................
An expression is defined as a set of numbers, variables, and mathematical operations. The expressions can be arranged as shown below.
What is an Expression?In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.
According to the number of terms, the expressions can be arranged as,
Hence, the expressions can be arranged as shown above.
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If you want to make a comment that won’t be seen in r console (output) use .. what
#
print (“ “)
sum ()
rflip()
NO LINKS!! Please help me with this graph. Part 2
[tex]\large{\boxed{\sf y = \dfrac{2}{3} | x -6|- 7}}[/tex]
Explanation:Absolute value of a graph formula:
y = a |x -h| + kIdentify the vertex : (h, k) = (6, -7)
Take two points: (6, -7), (9, -5)
[tex]\sf Find \ slope \ (a) : \sf \ \dfrac{y_2 - y_1}{x_2- x_1} \ = \ \ \dfrac{-5-(-7)}{9-6} \ = \ \ \dfrac{2}{3}[/tex]
Join them to build the equation: [tex]\bf{y = \dfrac{2}{3} |x - 6| - 7}[/tex]
Answer:
[tex]g(x)=\dfrac{2}{3}|x-6|-7[/tex]
Step-by-step explanation:
Translations
For [tex]a > 0[/tex]
[tex]f(x-a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units right}[/tex]
[tex]f(x)-a \implies f(x) \: \textsf{translated}\:a\:\textsf{units down}[/tex]
[tex]y=a\:f(x) \implies f(x) \: \textsf{stretched parallel to the y-axis by a factor of}\:a[/tex]
-----------------------------------------------------------------------------------------
Parent function: [tex]f(x)=|x|[/tex]
[tex]f(0)=|0|=0 \implies \textsf{The vertex of the parent function is at (0, 0)}[/tex]
From inspection of the graph, the vertex of the transformed function is at (6, -7). Therefore, there has been a translation of:
6 units right7 units down[tex]\textsf{6 units right}\implies f(x-6) =|x-6|[/tex]
[tex]\textsf{and 7 units down}\implies f(x-6)-7=|x-6|-7[/tex]
From inspection of the graph, we can see that it has been stretched parallel to the y-axis:
[tex]\implies a\:f(x-6)-7=a|x-6|-7[/tex]
The line goes through point (0, -3)
Substituting this point into the above equation to find [tex]a[/tex]:
[tex]\implies a|0-6|-7=-3[/tex]
[tex]\implies 6a=4[/tex]
[tex]\implies a=\dfrac{2}{3}[/tex]
Therefore,
[tex]\implies g(x)=\dfrac{2}{3}|x-6|-7[/tex]
9 hundreds 5 ten thousands
9 ones
Answer:
50,909
Sort the digits out from greatest to least, and form a number.
The number 92,581 is represented in standard form as the sum of its place values: 90,000 + 2,000 + 500 + 80 + 1.
Standard form is a way to represent numbers using digits.
In standard form, each digit's value is determined by its position in the number.
Given 9 ten thousands + 2 thousands + 5 hundreds + 8 tens + 1 one.
9 ten thousands means we have 9 sets of ten thousands, which is 9 × 10,000 = 90,000.
2 thousands means we have 2 sets of thousands, which is 2 × 1,000 = 2,000.
5 hundreds means we have 5 sets of hundreds, which is 5 × 100 = 500.
8 tens means we have 8 sets of tens, which is 8 × 10 = 80.
1 one is the value 1.
Now, let's add up all these values:
90,000 + 2,000 + 500 + 80 + 1
= 92,581.
So, the number 92,581 is represented in standard form as the sum of its place values: 90,000 + 2,000 + 500 + 80 + 1.
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Complete question:
Write the number in standard form.
9 ten thousands +2 thousands +5 hundreds + 8 tens +1 one
Ask an expert 2+3/10X>=13/20 Solve for inequality Thanks!
Answer:
The answer is in the picture.
Step-by-step explanation:
[tex]2+\frac{3}{10x}\geq\frac{13}{20} \\\\\frac{3}{10x}\geq\frac{13}{20} -2 \\\\\frac{3}{10x}\geq\frac{13}{20} -\frac{40}{20} \\\\\frac{3}{10x}\geq-\frac{27}{20} \\\\3\geq-\frac{27}{20}*10 x \\\\3\geq-\frac{270}{20} x\\\\3\geq-\frac{27}{2} x \\\\3*-\frac{2}{27} \leq x\\\\-\frac{6}{27} \leq x\\\\-\frac{2}{9} \leq x[/tex]
Also x cannot equal to 0 if you plug in into the original equation the answer is indefinite/not solution.
4x4 y3 + v y + 7
Leading term:
Leading coefficient:
Constant term:
Answer:
Leading term: 4x⁴y³
Leading coefficient: 4
Constant term: 7
The leading term contains the highest degree and power of variable.The leading coefficient is the number written in front of the variable with the largest exponent.The constant term is the simplified number written where there are no variables.Answer:
Leading terms : 4x⁴y³
Leading co-efficient: 4
Constant: 7
Step-by-step explanation:
Leading term: Leading term is the term that holds the highest degree of the polynomial.
Leading co-efficient is the coefficient of the leading term.
Constant term is the term without any variable
Please help me with my question!
When we add two negative numbers, the result will be negative.
When we add a negative and a positive number, the result can be positive, negative, or equal to zero.
Take the absolute values of both numbers (disregard their signs). If the number that was positive is greater, then the result will be positive.If the number that was negative is greater, then the result will be negative.If the two numbers are equal, then the result will be 0.When we add two positive numbers, the result will be positive.
Solving the Questionj + k
These are both negative numbers. We know this because they are both to the left of 0. When we add two negative numbers, we will get a result that is less than 0.
Less than 0k + n
k is a negative number while n is a positive number.
Notice that on the number line, k and n appear to be at a equal distance away from 0. This means that if we were to take their absolute values, they would be equal.
This means that adding k and n would result in an answer of 0.
Equal to 0m + n
m is a negative number while n is a positive number.
Notice that on the number line, n appears to be further away from 0 than m is. m is very close to 0.
This means that the absolute value of n would be greater than that of m. The result would therefore be positive
Greater than 0k + m
Both these numbers are negative. Adding them would produce a negative result.
Less than 0